karadda said:oh, I am not too sure what to do with it. i understand that the limit goes to infinity, UNLESS x = 1/2 in which case it goes to 0. how do i proceed knowing that?
nm, i should just stop there ;)
1/2 is the only value of x for which this will converge, so the interval of convergence is {1/2}. the radius is 0.
The radius of convergence is a value that indicates the interval within which a power series converges. It is typically denoted by the letter "R" and can be calculated using the ratio test or the root test.
The radius of convergence is determined by examining the coefficients of the terms in the power series. The ratio test or the root test can then be used to find the limit of the terms, which will give the radius of convergence.
The radius of convergence tells us the values of x for which the power series will converge. If x is within the radius of convergence, the series will converge. If x is outside the radius, the series will diverge.
No, the radius of convergence must be a positive value. It represents the distance from the center of the power series to the closest point at which the series will converge. A negative value would not make sense in this context.
The radius of convergence can be used to determine the interval of convergence for a power series. It can also help in determining the convergence or divergence of a series and can be used to approximate functions within the interval of convergence.